scholarly journals Robust Assessing the Lifetime Performance of Products with Inverse Gaussian Distribution in Bayesian and Classical Setup

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Abdullah Ali H. Ahmadini ◽  
Amara Javed ◽  
Sohail Akhtar ◽  
Christophe Chesneau ◽  
Farrukh Jamal ◽  
...  
Keyword(s):  
Diffusion Processes ◽  
Data Distribution ◽  
Estimation Procedure ◽  
Potential Candidate ◽  
Posterior Distributions ◽  
Inverse Gaussian ◽  
Noninformative Priors ◽  
Credible Intervals ◽  
Model Diffusion ◽  
Two Parameter

The inverse Gaussian (Wald) distribution belongs to the two-parameter family of continuous distributions having a range from 0 to ∞ and is considered as a potential candidate to model diffusion processes and lifetime datasets. Bayesian analysis is a modern inferential technique in which we estimate the parameters of the posterior distribution obtained by formally combining a prior distribution with an observed data distribution. In this article, we have attempted to perform the Bayesian and classical analyses of the Wald distribution and compare the results. Jeffreys' and uniform priors are used as noninformative priors, while the exponential distribution is used as an informative prior. The analysis comprises finding joint posterior distributions, the posterior means, predictive distributions, and credible intervals. To illustrate the entire estimation procedure, we have used real and simulated datasets, and the results thus obtained are discussed and compared. We have used the Bayesian specialized Open BUGS software to perform Markov Chain Monte Carlo (MCMC) simulations using a real dataset.

scholarly journals Two-parameter diffusion processes and martingales

1983 ◽  
Vol 15 (1) ◽  
pp. 31-57 ◽  
Author(s):  
D. Nualart
Keyword(s):  
Diffusion Processes ◽  
Two Parameter

scholarly journals Inference of stress-strength reliability for two-parameter of exponentiated Gumbel distribution based on lower record values

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0249028
Author(s):  
Ehsan Fayyazishishavan ◽  
Serpil Kılıç Depren
Keyword(s):  
Information Matrix ◽  
Gumbel Distribution ◽  
Sampling Technique ◽  
Real Data ◽  
Record Values ◽  
Unknown Parameters ◽  
Data Set ◽  
Credible Intervals ◽  
Lower Records ◽  
Two Parameter

The two-parameter of exponentiated Gumbel distribution is an important lifetime distribution in survival analysis. This paper investigates the estimation of the parameters of this distribution by using lower records values. The maximum likelihood estimator (MLE) procedure of the parameters is considered, and the Fisher information matrix of the unknown parameters is used to construct asymptotic confidence intervals. Bayes estimator of the parameters and the corresponding credible intervals are obtained by using the Gibbs sampling technique. Two real data set is provided to illustrate the proposed methods.

scholarly journals The fallacy of placing confidence in confidence intervals - A commentary

2017 ◽  
Author(s):  
Jose D. Perezgonzalez
Keyword(s):  
Confidence Intervals ◽  
Common Ground ◽  
Posterior Distributions ◽  
Correct Interpretation ◽  
Psychonomic Bulletin ◽  
Credible Intervals ◽  
Per Se

‘The fallacy of placing confidence in confidence intervals’ (Morey et al., 2016, Psychonomic Bulletin & Review, doi: 10.3758/s13423-015-0947-8) delved into a much needed technical and philosophical dissertation regarding the differences between typical (mis)interpretations of frequentist confidence intervals and the typical correct interpretation of Bayesian credible intervals. My contribution here partly strengthens the authors’ argument, partly closes some gaps they left open, and concludes with a note of attention to the possibility that there may be distinctions without real practical differences in the ultimate use of estimation by intervals, namely when assuming a common ground of uninformative priors and intervals as ranges of values instead of as posterior distributions per se.

Gibbs Sampling Method in the Multidimensional Logistic Response Model with Missing Responses

2014 ◽  
Vol 926-930 ◽  
pp. 3830-3833
Author(s):  
Zhi Hui Fu ◽  
Cui Xin Peng ◽  
Bin Li
Keyword(s):  
Missing Data ◽  
Logistic Model ◽  
Sampling Method ◽  
Missing Values ◽  
Data Augmentation ◽  
Posterior Distributions ◽  
Missing Responses ◽  
Bayesian Paradigm ◽  
Item Parameters ◽  
Two Parameter

Missing data are often a problem in statistical modeling. How to estimate item parameters with missing data in item response theory (IRT) is an interesting issue. The Bayesian paradigm offers a natural model-based solution for this problem by treating missing values as random variables and estimating their posterior distributions. In this article, based on a data augmentation scheme using the Gibbs sampler, we propose a Bayesian procedure to estimate the multidimensional two parameter Logistic model with missing responses.

QUASI-INDIRECT INFERENCE FOR DIFFUSION PROCESSES

1998 ◽  
Vol 14 (2) ◽  
pp. 161-186 ◽  
Author(s):  
Laurence Broze ◽  
Olivier Scaillet ◽  
Jean-Michel Zakoïan
Keyword(s):  
Diffusion Processes ◽  
Asymptotic Properties ◽  
Estimation Procedure ◽  
Indirect Inference ◽  
Sampled Data ◽  
Finite Sample ◽  
Inference Procedure ◽  
Monte Carlo Experiments ◽  
Simulation Step ◽  
Finite Sample Properties

We discuss an estimation procedure for continuous-time models based on discrete sampled data with a fixed unit of time between two consecutive observations. Because in general the conditional likelihood of the model cannot be derived, an indirect inference procedure following Gouriéroux, Monfort, and Renault (1993, Journal of Applied Econometrics 8, 85–118) is developed. It is based on simulations of a discretized model. We study the asymptotic properties of this “quasi”-indirect estimator and examine some particular cases. Because this method critically depends on simulations, we pay particular attention to the appropriate choice of the simulation step. Finally, finite-sample properties are studied through Monte Carlo experiments.

All Economics is Local: Spatial Aggregations of Economic Information

2016 ◽  
Vol 6 (3) ◽  
pp. 467-487 ◽  
Author(s):  
David Fortunato ◽  
Clint S. Swift ◽  
Laron K. Williams
Keyword(s):  
Diffusion Processes ◽  
Explanatory Power ◽  
Estimation Procedure ◽  
Economic Indicators ◽  
Economic Research ◽  
Media Report ◽  
Media Messages ◽  
Economic Information ◽  
National Economic ◽  
The Media

National economic indicators play a foundational role in political economic research, particularly in regards to electoral politics. Yet, scholars have failed to recognize that national economic indicators are simply aggregations of local economic information, and the manner in which they are aggregated may not be consistent with the process voters use to acquire, access, and incorporate economic information. We argue that the economic similarities among localities, and the way in which the media report on these similarities, provide more theoretically satisfying means of specifying how local information aggregates into an overall portrait of the national economy. We introduce a novel estimation procedure called the spatial-X ordered logit that offers the chance to model how voters’ evaluations respond to changes in contextualized economic information. Our results support our theory that voters incorporate economic information from other localities with similarly structured economies and in ways that are shaped by media messages. Furthermore, these two specifications offer greater explanatory power than national indicators and other geographical means of aggregating economic information. We conclude by offering a number of implications for research questions ranging from electoral accountability to spatial diffusion processes.

PRICING OF FIRST TOUCH DIGITALS UNDER NORMAL INVERSE GAUSSIAN PROCESSES

2006 ◽  
Vol 09 (06) ◽  
pp. 915-949 ◽  
Author(s):  
OLEG KUDRYAVTSEV ◽  
SERGEI LEVENDORSKIǏ
Keyword(s):  
Diffusion Model ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
Spot Price ◽  
Inverse Gaussian ◽  
Jump Diffusion Processes ◽  
Double Exponential ◽  
Motion Approximation ◽  
Jump Diffusion Model ◽  
Normal Inverse Gaussian

We calculate prices of first touch digitals under normal inverse Gaussian (NIG) processes, and compare them to prices in the Brownian model and double exponential jump-diffusion model. Numerical results are produced to show that for typical parameters values, the relative error of the Brownian motion approximation to NIG price can be 2–3 dozen percent if the spot price is at the distance 0.05–0.2 from the barrier (normalized to one). A similar effect is observed for approximations by the double exponential jump-diffusion model, if the jump component of the approximation is significant. We show that two jump-diffusion processes can give approximately the same results for European options but essentially different results for first touch digitals and barrier options. A fast approximate pricing formula under NIG is derived.

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